On 5/27/2013 10:51 AM, Charlie-Boo wrote:> On May 26, 2:52 am, Zuhair <zaljo...@gmail.com> wrote:>> Frege wanted to reduce mathematics to Logic>> What does it mean to "reduce mathematics to Logic"?

Historically, mathematics had been seen as treating the scienceof number and the science of form. Classes had been consideredthe subject of logic. As mathematics developed in the 19thcentury, issues associated with geometry motivated a generalarithmetization of mathematics. The Fregean program oflogicism involved establishing the foundations of mathematicsby defining arithmetic in terms of classes.

A more modern author who makes a simple statement of suchis Quine in "Methods of Logic" if I recall correctly.

> The comments I> see after this first post seem to debate what that means, as well. If> (since) you are going to give (giving) a formal answer, then what is> the formal problem? Trigonometry is part of Mathematics. How would> we "reduce trig to Logic"? Or start with a simple case: What is the> criteria for something said to reduce number theory to logic?>> Computers process only zeros and ones. Anything you do on paper can> be done with a computer. If 0 is replaced by FALSE and 1 is replaced> by TRUE, does a computer reduce mathematics to logic?>

Actually, Boole's idea had been to address issuesin logic more mathematically. So, your examplereflects replacing the traditional semanticalnotions of logic with the Boolean arithmeticalrepresentation.

This is opposite to what you ask.

Sometimes one sees reference to Boole as beingassociated with an algebraic approach to logic(a Boolean algebra is a logical algebra, right?)in contrast to the symbolic approach to logicassociated with philosophical treatments.

I would probably classify your reference towhat can be done "on paper" along the linesof a symbolic approach, and, the Russianschool of constructive mathematics is explicitin their treatment of number along such lines.